Circulatory Fidelity began as a diagnostic for variational inference failure and grew into a unified framework for measuring relational structure across scientific domains. It is an independent research program in active development.
The core insight is simple: when you factorize a system into independent parts, you pay an information-theoretic cost proportional to the relational structure you discarded. IC (Inference Coupling) measures this cost from model structure alone, before inference.
What started as a single metric for a single problem — detecting when mean-field variational inference would fail — turned out to connect deeply to information geometry, thermodynamics, quantum information, spectral graph theory, and dozens of other domains. The connections are not analogies: the same mathematical objects appear independently in each field, measured by the same IC.
CF is grounded in an explicit ontological commitment to relational primacy — the position that patterns of relation are primary and nodes are emergent. This is not decorative philosophy: it generates specific predictions that are confirmed by data across 50,000+ validation observations.
CF v1.1 is published on Zenodo (DOI: 10.5281/zenodo.18121821). Three papers are in preparation for simultaneous arXiv release. The framework spans 41 domains across 4 tiers of validation strength, with 154 formally characterized cross-domain connections.
The framework emerged from studying where Bayesian computation fails — specifically, mean-field variational inference applied to systems with significant coupling. The diagnostic question "when does factorization cost too much?" turned out to have answers far beyond the inference context where it was first asked.
Three papers are in preparation for simultaneous arXiv release. Each stands alone for its target audience while cross-referencing the others for depth.
Core MFVI diagnostic — IC definition, Relational Invariance theorem, validation studies, practical workflow. For Bayesian practitioners who need to know when their factorized inference will fail.
Control Coupling taxonomy, observer-dependence, and screening effects. How coupling strength varies by layer depth, and why the nearest layer always dominates. For researchers working with deep hierarchical models.
Detection of higher-order relational structure invisible to pairwise analysis. Walsh-Hadamard protocol, encoding-relativity, and the GF(2)–stabilizer correspondence. For anyone working with systems where pairwise methods fail unexpectedly.
Connects IC to spectral graph theory: the second eigenvalue λ₂ of the frustration graph tracks satisfiability phase transitions and proof complexity bounds. Formal width/size lower bounds for resolution refutations via IC thresholds. Separate manuscript in preparation.
@software{lowry2025circulatory,
author = {Lowry, Aaron},
title = {Circulatory Fidelity: A Diagnostic
Framework for Relational Structure},
year = {2025},
version = {1.1},
doi = {10.5281/zenodo.18121821},
url = {https://circulatoryfidelity.com}
}
The research is conducted within a distributed laboratory architecture spanning 41 domains across 4 tiers of validation strength. Each domain maintains its own state, operationalization, and validation pipeline. The network of 154 cross-domain connections is formally characterized — not asserted by analogy but demonstrated through shared mathematical structure.
From variational inference and information geometry (Tier 1, fully validated) through cognitive science and bioelectric theory (Tier 2, structurally established) to causal inference and chemistry (Tier 3, early-stage) and quantum gravity (Tier 4, speculative). Each domain is classified by a composite score reflecting formal, empirical, and operational soundness.
Connections between domains are not hand-waved analogies. Each edge in the network represents shared mathematical objects — the same IC, the same geodesic coordinate, the same cost function — appearing independently in each domain. The stabilizer/coset decomposition separates what transfers between domains (IC values, coupling regime, cost function — the universal structure) from what is domain-specific (node identity, measurement protocol, physical interpretation — reconstructed locally in each field).
Every claim within the laboratory carries an explicit STQA class (proven, structural, analogical) and pipeline stage (substrate, computed, predicted, confirmed). Mathematical identities are never conflated with empirical claims; structural correspondences are never confused with casual analogies.
Explore the full domain network on the Domains page.
CF diagnostics are available in Python and Julia. MIT licensed. Designed for integration into existing Bayesian workflows.
from circulatory_fidelity import inference_coupling, diagnose # Estimate IC between latent and observed ic, se = inference_coupling(z_samples, x_samples) # Full diagnostic workflow result = diagnose(z, x, model_type='filtering') print(f"IC = {result['ic']:.3f}") print(f"Risk: {result['risk_level']}") print(f"MSE ratio: {result['mse_ratio']:.2f}")
using CirculatoryFidelity # Estimate IC from samples ic, se = inference_coupling(z, x) # Closed-form for Gaussian systems ic = ic_gaussian(ρ) # Two-stage coplexity detection result = two_stage_protocol(X, y) println("Pairwise IC: $(result.ic2)") println("Coplex IC: $(result.ic3)")
CF is in active development. Collaboration inquiries, technical questions, domain extension proposals, and critical engagement are welcome.